Amorphous polymers are important engineering materials; however, their nonlinear, strongly temperature- and rate-dependent elastic-viscoplastic behavior is still not very well understood, and is modeled by existing constitutive theories with varying degrees of success. There is no generally agreed upon theory to model the large-deformation, thermo-mechanically coupled response of these materials in a temperature range which spans their glass transition temperature. Such a theory is crucial for the development of a numerical capability for the simulation and design of important polymer processing operations, and also for predicting the relationship between processing methods and the subsequent mechanical properties of polymeric products. We have developed a large-deformation thermo-mechanically coupled elastic-viscoplastic theory for thermoplastic amorphous polymers and shape memory polymers which spans their glass transition temperature. The theory has been specialized to represent the major features of the thermo-mechanical response of three technologically important thermoplastic amorphous polymers - a cyclo-olefin polymer (Zeonex-690R), polycarbonate, poly(methyl methacrylate) and a representative thermoset shape memory polymer - in a temperature range from room temperature to approximately 40 C above the glass transition temperature of each material, in a strain-rate range of ~ 10-4 to 101 s-1, and compressive true strains exceeding 100%. Our theory has been implemented in the finite element program ABAQUS. In order to validate the predictive capability of our constitutive theory, we have performed a variety of macro- and micro-scale validation experiments involving complex inhomogeneous deformations and thermal processing cycles. By comparing some key features, such as the experimentally-measured deformed shapes and the load-displacement curves from various validation experiments against corresponding results from numerical simulations, we show that our theory is capable of reasonably accurately reproducing the results obtained in the validation experiments.